PSAT Practice Test 1 — Personalized Study Plan

1. Quadratics — the single biggest weak spot Highest priority

Missed: M1 Q14 · M2 Q5, Q13, Q15, Q16, Q19, Q20, Q22 (8 questions)

Almost half of Math errors involve a quadratic in some form. Every sub-skill here appeared: reading a quadratic off a table, discriminant conditions, factoring form, sum/product of roots (Vieta's), completing the square for circles, vertex form.

• Master the discriminant: b²−4ac < 0 → no real solutions, = 0 → one solution, > 0 → two solutions. Two of the missed grid-ins hinged on this.
• Complete the square on sight — including in circle equations of the form x²+x+y²+y=k (Q20). Practice until it's automatic.
• Vieta's formulas: for ax²+bx+c=0, sum of roots = −b/a, product = c/a. This unlocks Q19 quickly.
• Vertex form ↔ standard form: know how to move between y=a(x−h)²+k and y=ax²+bx+c, and what each parameter tells you.
• Building a quadratic from a table of values: plug three points into y=ax²+bx+c and solve the system (Q5).

2. Exponential functions & growth models High

Missed: M1 Q14, Q19 · M2 Q10 (3 questions)

• Understand the standard form P(t) = P₀ · r^t and be able to translate between growth per period and per unit time (Q10 uses r=1.0446 per year — asks for % per period).
• Distinguish arithmetic vs. geometric sequences: "each term is 4 times the preceding" → geometric, so wₙ = 9·4^(n−1).
• Doubling problems: if quantity doubles every k time units, model is P·2^(t/k).

3. Linear equations & systems — "no solution" / translations Medium

Missed: M1 Q6, Q9, Q18, Q22 · M2 Q4, Q11 (6 questions)

• No solution = same slope, different y-intercept (parallel lines). Q18 & Q11 both test this. Rewrite each equation into y = mx + b form and compare.
• Translating a line down k units: subtract k from the y side, i.e. y becomes y+k in the equation. Then set y=0 to find the new x-intercept (Q22 M1).
• Simple algebra like 4x−4=112 (Q9) was missed — likely a rushed step. Slow down and re-read what's being asked (x−1, not x).
• Read grid-in prompts twice. Q6 asks for a valid combination given constraints, not just any x — get every question's ask nailed before solving.

4. Function evaluation & rational/asymptotic behavior Medium

Missed: M2 Q6, Q18 (2 questions)

• For f(x) with fractional/rational forms, substitute carefully and isolate the variable step-by-step.
• Recognize graphs of rational functions: vertical asymptote → denominator zero; horizontal asymptote → ratio of leading coefficients.

5. Exponent rules & percent change Refresh

Missed: M1 Q16 (exponents), Q17 (percent)

• Fractional exponents: x^(1/n) = ⁿ√x; x^(a/b) = (x^a)^(1/b). Rewrite radicals as fractional exponents to combine cleanly.
• A 7% increase means multiplying by 1.07 (not 0.07 or 107). This is a one-line fix but it cost a point.

1. Transitions & text-structure logic Highest R&W priority

Missed: M1 Q7, Q21 · M2 Q3, Q26 (4 questions)

• Before picking the transition, write one word in the margin describing the relationship between the two sentences: contrast, cause, example, addition, sequence. Then match to the choices.
• "However / but / yet" signal contrast; "therefore / thus / as a result" signal cause; "for example / for instance" signal illustration; "moreover / furthermore" signal addition.
• Beware of transitions that are grammatically fine but logically wrong for the paragraph — that's exactly how these were missed.

2. Vocabulary in context Medium

Missed: M1 Q1 (hinder), Q3 (haphazard) — both in the first three questions of the test

• Predict before you peek. Cover the choices, read the sentence, and put your own word in the blank. Then match.
• Watch for "didn't ___" phrasing — the blank's meaning inverts. Q1 got missed likely because "aggravate" felt like a strong contrast word without checking meaning.
• Build a running list of "context" words missed (hinder, haphazard so far) — review these before the next test.

3. Grammar & punctuation (Rules-of-thumb section) Medium

Missed: M2 Q19, Q21, Q22 (3 questions)

• Semicolon = period-lite: both sides must be independent clauses. Comma alone between two independent clauses = comma splice.
• Subject-verb agreement across long prepositional phrases: strip the middle to see the real subject.
• Verb tense should be consistent with the surrounding paragraph's timeframe unless a clear signal shifts it.

4. Inference / main idea / purpose Medium

Missed: M1 Q12, Q18 · M2 Q1, Q16, Q22 (5 questions)

• The correct answer is always supportable from the text alone. If a choice requires outside knowledge or one extra assumption, it's wrong — even if it sounds true.
• Eliminate choices that are too extreme (always, never, first, only) or too narrow (mention one detail but miss the main point).

5. Data / graph interpretation Refresh

Missed: M1 Q11 · M2 Q12 (2 questions)

• Read axis labels and units first. Then locate the exact data point the question refers to before looking at the choices.
• The correct choice must be both accurate and relevant to the claim — sometimes a choice is factually right but doesn't support the specific argument.